Simplify the following expression: $ n = \dfrac{1}{7} - \dfrac{-4k}{k - 1} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k - 1}{k - 1}$ $ \dfrac{1}{7} \times \dfrac{k - 1}{k - 1} = \dfrac{k - 1}{7k - 7} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{-4k}{k - 1} \times \dfrac{7}{7} = \dfrac{-28k}{7k - 7} $ Therefore $ n = \dfrac{k - 1}{7k - 7} - \dfrac{-28k}{7k - 7} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{k - 1 + 28k }{7k - 7} $ Distribute the negative sign: $n = \dfrac{k - 1 + 28k}{7k - 7}$ $n = \dfrac{29k - 1}{7k - 7}$